The Scales of Justice: Keeping Equations Balanced

The Scales of Justice are a familiar symbol of fairness.

When both sides hold the same amount of weight, the scale remains balanced. If something changes on only one side, the scale tips.

An algebra equation works the same way. The equal sign tells us that the value on the left side is the same as the value on the right side. To keep an equation balanced, whatever we do to one side must also be done to the other.

The Brontos’ Mystery Weight

At the Dino Cove Courthouse, the Brontos discover a large balance scale.

On the left side of the scale is a mystery weight marked (x), along with one four-pound block.

On the right side are three four-pound blocks. Together, those three blocks weigh 12 pounds.

The scale is balanced, so we can write:

x+4=12

What is the value of the mystery weight?

Remove the Same Amount from Both Sides

The scale must remain balanced. To determine (x), remove—or subtract—the same amount from both sides.

The Brontos remove one four-pound block from the left side. They must also remove one four-pound block from the right side.

x+4-4=12-4

On the left side, adding 4 and then subtracting 4 cancel each other out. Only the mystery weight remains.

On the right side, two four-pound blocks remain. Together, they weigh 8 pounds.

x=8

The mystery weight weighs 8 pounds.

Check the Answer

A solution should always be checked. Replace (x) in the original equation with 8:

8+4=12

The left side equals 12, and the right side equals 12. Both sides are equal, The Brontos solved the mystery!

Just as the Scales of Justice represent fairness and equal treatment, an algebra equation stays balanced when the same operation is performed on both sides.